Table 1.

Optimal crop yield models for maize (ZeaL) and soybean (GlycL) production using the exponential form of logistic growth.

Crop	Fit	Variable	rmax	a	c	b	AICc	ΔAICc	wi	R2
ZeaL	L	tM/tMin	1.20	0.37**	−5.49**	12.58**	−22.03	0	0.97	0.80
	L	tmax/tMin	1.20	0.41**	−5.99**	10.32**	−12.12	9.91	0.01	0.78
	L	Shannon/tMin	1.20	0.53**	−4.76**	11.87**	−11.83	10.19	0.01	0.84
	L	Simpson/tMin	1.20	0.51	−4.55**	12.85**	−11.76	10.26	0.01	0.84
	P		1.20	0.93**	−7.91**		88.26	87.27	0	0.49
GlycL	V	Eevennes	0.97	0.63**	−4.09*	0.31*	−64.27	0	0.22	0.96
	V	Simpson	0.97	0.64**	−4.15*	0.31*	−64.11	0.16	0.20	0.96
	V	Shannon	0.97	0.65**	−4.19*	0.30*	−63.98	0.30	0.19	0.96
	V	Invsimp	0.97	0.65**	−4.27*	0.30*	−63.73	0.54	0.17	0.96
	V	Jevenness	0.97	0.64**	−4.11*	0.31*	−63.15	1.12	0.13	0.97
	V	Richness	0.97	0.71**	−4.80**	0.26*	−62.34	1.93	0.08	0.96
	P		0.97	1.95**	−15.23**		61.67	125.95	0	0.76

The best models were chosen by using multi-model selection methods described by Burnham et al. (2002) that compare a suite of candidate models using Akaike weights. We evaluated our basic model with internal processes (P) and the external perturbations of their parameters: r_max maximum finite reproductive rate (vertical model, V), a non-linearity coefficient (non-linear model, N), c the ratio between demand and offer of limiting resources (lateral model, L); with b coefficients for different external effects, AIC_c corrected Akaike information criterion, ΔAIC_c delta AIC_c and w_i Akaike weights of a set of selected models, and R² pseudo-coefficient of determination. Further description of the variables included in the models are given under “Materials and Methods” (here minimum -tMin-, mean -tM- and average maximum -tmax- temperature for growing season and weed community diversity indices –Shannon and Simpson indices-).

^**p < 0.01;

^*p < 0.05.